Factor Part 1
Factor:
7x^2 + 14x
7x(x+2)
Factor Completely:
x^3+4x^2+8x+32
4 terms, group to factor
(x^3+4x^2)+(8x+32)
x^2(x+4)+8(x+4)
(x+4)(x^2+8)
Factor Completely:
x^2-8x+12
Multiplies to 12:
-6 * -2
Adds to -8:
-6 + -2
(x-6)(x-2)
24a^2b^3+12a^3b
Factor:
12a^2b(2b^2+a)
Factor Completely:
25x^2-36
Both perfect squares and subtraction. Difference of Squares
(5x)^2-(6)^2
(5x+6)(5x-6)
Factor Completely:
-3y^2+6y+72
-3(y^2-2y-24)
Multiplies to -36:
4*-6
Adds to -2:
4+ -6
-3(y-6)(y+4)
Factor Completely:
x^2+4
Prime
This is not a difference of squares, its the SUM and no GCF so it cannot be factored.
Factor completely:
x^3+3x^2-4x-12
4 terms, group to factor
(x^3+3x^2)+(-4x-12)
[x^2(x+3)-4(x+3)]
(x+3)(x^2-4)
now we see the difference of squares
(x+3)[(x)^2-(2)^2]
(x+3)(x+2)(x-2)
Factor Completely:
6x^2-34x-40
2(3x^2-17x-20)
Multiplies to 3*-20 which is -60:
3*-20
Adds to -17:
3+ -20
2(3x^2+3x-20x-20)
2[3x(x+1)-20(x+1)]
2(x+1)(3x-20)
Factor Completely:
9x^2-42x+49
Front and back are perfect squares
(3x)^2-2(3x)(7)+(7)^2
Middle is =-42x, so its a perfect square trinomial:
(3x-7)^2